基于因果微积分定理讨论时域分析和s域分析

本文从因果微分定理、因果积分定理和拉氏变换出发,推导了拉氏变换中的时域微分性质、时域积分性质、初值定理和终值定理;系统时域分析是对系统微分方程使用因果微分定理得出的,而系统s域分析是对系统微分方程使用拉氏变换中的时域微分性质得出的,两者的原理和方法完全类似,我们对两者进行了全面的比较。这些分析和比较很有利于学生对拉氏变换中的几个重要性质的理解,也有利于学生明确系统时域分析与系统s域分析的区别与联系。

Discussion of the Time-Domain Analysis and S-Domain Analysis Based on the Causal Differential and Integral Theorem

The differential property,the integral property,the initial value theorem and the final value theorem in Laplace transformation are derived from the causal differential theorem,causal integral theorem and Laplace transformation in this paper.Because time-domain analysis technique is based on the causal differential theorem,and s-domain analysis technique is based on the differential property in Laplace transformation,i.e.the s-domain expression of the causal differential theorem,so their principles and methods are totally similar.Their comparison is thoroughly given.All of the derivation and comparison are very useful for students to well understand the discussed important properties in Laplace transformation as well as the differentiation and connection between time-domain analysis and s-domain analysis of LTI system.